Is glad to hear his health is improving. Has heard that JH is holding a large reception for all his descendents. Is progressing well with the book [on Francis Baily]. Sends a puzzle in spherical trigonometry.

Wishing him well for the new year. Hears JH has visited the East India College. Sends a theorem. H. P. Brougham (Baron Brougham and Vaux) amuses himself by finding the laws of central force for curves. Has been finding information on a nephew of Isaac Newton. George Stanhope (6th Earl of Chesterfield) and T. A. W. Parker (9th Earl of Macclesfield) were pupils of Abraham De Moivre.

Has not heard from him for a long time. Thought that the Government was going to turn the R.A.S. out of Somerset House. There is someone to come to the rescue of Richard Sheepshanks. Has not seen Charles Babbage for many years. Their views are incompatible. C. P. Smyth is off to Teneriffe so now is the time for JH to make suggestions. Has set up a committee to make by-laws.

Comments on the state of JH's health, and on things astronomical and mathematical.

Is glad to hear his account of facts. Always thought he would recover his health. Gives one of his own mathematical formulae. Has no idea how the Decimal Coinage Commission is progressing.

Would he answer some of his queries when he has leisure? Queries on the law of beats for unison sounds. Met JH's daughter on Monday, who gave a fair account of JH and his recent work.

Wants to make a new musical instrument on the principle of resonance; JH also suggests some improvements in the construction of the organ.

Has long held the view that a pipe underneath the strings of a piano would increase the resonance. Had not conceived such an instrument as JH suggested. Why are 3rds and 6ths more agreeable to the ear than 4ths and 5ths?

Sending a pamphlet, which may give JH some amusement.

JH's last letter was written in a good strong hand. Recommends suitable drink for hot weather. Gives his views about the possible marriage of Isaac Newton's niece. Has had a letter from a Mr. Wither on mathematical books.

Many thanks for his invitation, but he does not intend going to Eastbourne. Further remarks on his own theory regarding the marriage of Isaac Newton's niece.

Has fallen from a ladder in his library and dislocated his shoulder, which accounts for the form of his letter. Has he any recollections of Humphry Davy rubbing his hands together?

Thought that AD's last letter was supposed to be written in verse. Hopes his injury will soon improve. Does not recollect any habit of Humphry Davy rubbing his hands together. A professor, [G. J.?] Stoney, has re-invented JH's collimating telescope and not improved it.

Quotes a rhyme. May have been injured even if he had been at Collingwood. Possibly [G. J.?] Stoney has not read JH on the telescope. Is thriving in health but sleeping very well.

Hopes his health is improving as his own is. Saw Henry Warburton last week. Gives one of his own theorems. Sends a lecture on the decimal coinage.

Comments on the state of JH's health, color blindness, missing R.A.S. Notices, and decimal coinage.

Pleased to hear his health is improving, but he should rest in the morning. Thinks it will be a long time before the decimal coinage can be introduced. Comments on cooking in the next century. Has been looking at a 10" bar of aluminum, which [Thomas?] Graham has sent him.

Thanks for the magic square, which he is now returning. Seems no end to the possibilities of such squares.

Offers AD a puzzle and JH's solution to AD's problem about a body revolving in the evolute of an ellipse. On sending Francis Baily's correspondence to Greenwich.

JH has got hold of the explanation about central forces. Need not worry about Elizabeth Baily; he will see to that. Do not reject any letters; they may be important in the future. Gives one of his own theorems.